Elastic Equilibrium of Seuii-Infinito Solid. 



21 



iVi being greater tlian N.2 and N:- which are equal. Thus the 

 stress quadric at any point in the interior is a spheroid, of whicli 

 the axis of rotation lies in a plane passing through the 2;-axis. 



If we denote by D the difference of the greatest and the least 

 principal stresses, tlien 



77 Sz 



D = N,-N...= — 



2- (r' + (z + afr^' 

 D is a maximum at the point (r=0, ^ = -|-J and its value is 



(50) 



B,.o.. = 



2/7 



9-r 



(51) 



wliile iV'^i, the greatest princi})al stress, is a maximum at the point 

 (r = 0, ^ = 0) and 



n 



N = 



"lûïCl? 



(52) 



Thus the latter maximum is greater than the former, and, more- 

 over, the position where the rupture might occur is quite different 

 for the two hypotheses: it is at a certain distance ])elow tlie surface 

 in the former, while it is at the surface in tlie latter. 



In Fig. 3 it is shown liow tlie greatest principal stress and the 

 greatest difference of principal stresses along tlie .r-axis vary with 

 the depth from the surface. 



sAÇ 



D 



;x 



Eig. 3. 



